The function ##f(x) = \sqrt{1-e^{3x}}## does not have a series expansion in powers of ##x-a## when ##a = 0## (that is, a Maclauren expansion). The function ##f(x)## is real when ##x < 0## but is pure imaginary when ##x > 0##, and there is no way any function like that can have a Maclauren expansion.